A polygon mesh is a collection of vertices, edges, and faces that represent the surface of a three-dimensional object. Polygon meshes are often used to represent and manipulate three-dimensional surfaces in computer graphics and solid modeling applications. They are popular because they are flexible, expressive, and well-suited to manipulation using the accelerated graphics processing hardware that modern digital computers use. The data used to generate a polygon mesh can be understood as originating from either digitization of real-world objects, or from tessellation of synthetic data produced by a computer. Digitized data may be generated using hardware such as a three-dimensional range scanner, a surface scanner, or any other suitable device capable of evaluating a physical object. Tessellated data, on the other hand, may be generated using design software that applies implicit mathematical formulations, sketch-based modeling techniques, or any other suitable mathematical abstraction. However, regardless of the data source, a polygon mesh will often include characteristics such as holes, overlapping segments, disconnected segments, and self-intersecting polygons. These characteristics, which are often referred to as “defects”, can render the polygon mesh unsuitable for further processing using algorithms that, in general, may have specific quality and/or integrity requirements. For example, three-dimensional printing applications typically call for a closed mesh that is convertible to a solid model with well-defined internal and external regions. Defects such as gaps, holes, and self-intersecting polygons result in ambiguities that may cause a three-dimensional printing operation to fail. To address this challenge, a wide range of mesh repair techniques have been developed. Mesh repair can be understood as the process of modifying a polygon mesh to eliminate defects, thus satisfying the requirements of a particular application. Thus, for example, three-dimensional printing operations are often preceded by mesh repair operations. A wide range of mesh repair techniques are surveyed in Attene, et al., “Polygon Mesh Repairing: An Application Perspective”, ACM Computing Surveys, 45(2), Article 15 (February 2013), hereinafter referred to as “Attene”.